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I have a doubt on graph of $f(x) = \frac{x-5}{x+6}$. Is there a point of inflection on $x=-6$? The graph changes it nature from concave up to concave down but $f''(x)$ is not equal to zero anywhere.

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    $\begingroup$ $x = -6$ is not in the domain of $f$ so it cannot be considered as a point of inflection. $\endgroup$ – DeepSea Dec 5 '16 at 6:38
  • $\begingroup$ Yeah that's true. But as per the definition of point of inflection the concativity changes so isn't that be a point of inflection? will there be any other point of inflection for this graph? $\endgroup$ – Rohit Gulabwani Dec 5 '16 at 6:41
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    $\begingroup$ there is none ! $\endgroup$ – DeepSea Dec 5 '16 at 6:42
  • $\begingroup$ Concavity is opposite on disjoint intervals. There is no inflection point, nor is one required to exist. $\endgroup$ – dxiv Dec 5 '16 at 6:46
  • $\begingroup$ If a graph is defined for x>=0 so can x=0 have a relative maxima or minima? $\endgroup$ – Rohit Gulabwani Dec 5 '16 at 6:53
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There won't be any point of inflection as at x = -6 the function is undefined.

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